Nowadays many companies have available large amounts of raw, unstructured data. Among Big Data enabling technologies, a central place is held by the MapReduce framework and, in particular, by its open source implementation, Apache Hadoop. For cost effectiveness considerations, a common approach entails sharing server clusters among multiple users. The underlying infrastructure should provide every user with a fair share of computational resources, ensuring that service level agreements (SLAs) are met and avoiding wastes. In this paper we consider mathematical models for the optimal allocation of computational resources in a Hadoop 2.x cluster with the aim to develop new capacity allocation techniques that guarantee better performance in ...